My parents had similar work done quite a few years ago now, instead of creating a new gable, they just extended a roof from the exiting ridge out over the extension at a shallower pitch than the existing. In their case the extension did not project that much from the existing house, if yours does, this may not be an option.
It would probably be a good idea to get a few quotes from some actual builders and then determine if the cost would be justified by the benefits to your quality of life.
Leo